Canvas paper can be mounted the usual ways, so if you are using a T-hinge or V-hinge to a backing board, then there is no need for coating, especially if you are then glazing. Canvas paper can’t be stretched.
Canvas being different, it is a cloth not a paper, and is flexible and can be stretched. Stretching can cause cracking at the edge of the stretcher bars.
It is always better to coat canvas, unless you are maybe dry mounting. I have used Innova ‘Ultra Gloss’ (which isn’t ultra glossy, but more glossy than matte canvas) without coating. Breathing Color Crystalline also claims no need for coating.
In general, easy wrap systems distribute the stress better when stretching, but you need a padded surface to lessen the chance of abrasion at the edges.
Brian A